State-of-the-art high-speed optical transceivers designed for multimode fiber optic cable (MMF) transmission use Vertical Cavity Surface Emitting Lasers (VCSELs) as light sources. VCSELs, like conventional Light Emitting Diodes (LEDs) are surface emitting devices; but unlike LEDs the physical structure of a VCSEL comprises a layer of multiple quantum wells between Bragg Reflectors forming a laser cavity. As a result, the output of the VCSEL is highly coherent, comprising discrete optical modes. The device supports a single longitudinal mode coupled with multiple transverse modes resulting in a distribution of light with slightly different wavelengths. In addition, each mode has a defined emission pattern. This physical effect results in an emission pattern in which the emitted wavelength is radius-dependent. The VCSEL modes are also dynamic, and in combination with the optical properties of MMF cause variability in MMF system performance. Performance variations can be attributed to MMF core defects and modal dispersion effects.
Most MMFs contain one or more core defects resulting from variations in gas flow control during the fabrication process. It is possible to modify the refractive index profile such that process variations produce a refractive index profile or bias that compensates for the effect of wavelength dependent VCSEL emission patterns that will improve fiber performance. To determine the optimum index profile with no core defects, one must first consider the optical modes emitted by a VCSEL. With reference to FIG. 1, exited optical modes are shown as a function of drive current for a representative VCSEL.
Due to the crystal structure and circular symmetry of the device, there are two polarization states for each excited transverse mode in a VCSEL. The electric field orientation defines the polarization state of the optical mode. When the drive current is turned on (5 mA), the fundamental mode is excited near the center of the device. As the drive current is increased, more modes (higher-order modes) are excited, which occupy the outer regions of the active area or aperture of the device. Each mode has a discrete optical energy and is therefore characterized by a discrete optical wavelength given by, E=hc/λ, where h=Planck's constant and c is the speed of light. Lower-order modes have longer wavelengths whereas higher order modes have shorter wavelengths and higher energy. This correlation between mode and wavelength is illustrated in FIG. 2. The fundamental mode is shown to have the longest wavelength and higher-order modes have shorter wavelengths.
Due to the radially dependent wavelengths of the VCSEL modes, the modes that propagate in the fiber also have a wavelength dependence. Lower-order VCSEL modes couple into lower-order fiber modes, whereas higher-order VCSEL modes couple into higher-order fiber modes. This wavelength dependence is demonstrated in the optical spectral analysis shown in FIG. 3. In this analysis, a MMF is connected to a high-speed optical transmitter containing a VCSEL. A single-mode fiber (SMF) having a core diameter of 5 microns (SMF for 850 nm) is scanned across the output end of the MMF. Using an Optical Spectrum Analyzer (OSA), the optical spectrum of the modes is recorded as a function of radial displacement. There are typically five or more primary wavelengths emitted by a VCSEL. In the region of each primary wavelength there are typically several closely spaced wavelengths generated by other modes or polarization states.
We see in FIG. 3 that as the lateral offset increases, the relative optical power carried by the longer wavelengths (near 849.33 nm) diminishes, while the relative power of the shorter wavelengths (near 848.1 nm) increases. It is also observed that there is an overall shift to shorter wavelengths at large radial offsets. As a result of this radial distribution of the spectrum, the optical pulse at zero offset has a longer RMS center wavelength than at larger radial offsets, as indicated in FIG. 4 by the arrows. The center wavelength, λc, is the RMS weighted average of the optical peaks given by,
                              λ          c                =                                            ∑                              i                =                1                            N                        ⁢                                          P                i                            ⁢                              λ                i                                                                        ∑                              i                =                1                            N                        ⁢                          P              i                                                          (        1        )            
Although the spectral distribution of VCSEL modes may vary from device to device, the physics of the device remain unchanged and a nominal radial distribution can be approximated. Using a representative VCSEL radial distribution in combination with the spatial coupling into guided fiber modes, it is possible to improve the refractive index profile of a MMF to reduce modal dispersion, improving MMF performance. Thus, it would be desirable to have a new refractive index profile that compensates for radially dependent wavelength emission patterns of laser sources in order to reduce modal dispersion in a MMF or other waveguides.